The significant past improvements of the rotary electric shaver have generally been focused on the shaver's ability to thread every hair end completely through a tiny opening in a metallic screen and cut it close to the skin as easily as done by the single stroke of a razor blade. However, the natural variation in growth angle of facial hair prevents the close-cutting of hair ends that are not positioned to fully penetrate the metallic screen during a single movement of the screen. Although rotary electric shavers can lift and push most hair ends into position for cutting, they cannot cut all hair ends underneath the perforated screens without multiple back-and-forth scrubbing movements of the shaver body. Because of this handicap, rotary shaver manufacturers recommend the use of circular movements of the shaver body in order to achieve a closer shave. This significant recommendation appears in the instruction manuals of all major rotary shaver manufacturers and is an unavoidable admission that a circular movement of the shaver's cutting head platform will produce a closer shave. Unfortunately, the circular and repeated straight movements of the shaver body are tiresome and particularly difficult over face areas that are not accessed easily, such as under the nose and chin and around the lips. These burdensome requirements for manipulation and irregular movements of the shaver body have continued to inhibit the wider acceptance and use of the rotary electric shaver. Many attempts to increase the efficiency of the multi-headed rotary shaver's cutting heads and overcome all the impediments to a closer shave have been described in earlier patents wherein various vibrating, arcuate and other modified circular movements of the shaving platform have been proposed without much success. The problem of achieving a close shave with minimal effort and only straight movements of the shaver body was not overcome until an uninterrupted circular rotation system for the shaving platform was introduced in U.S. Pat. No. 6,553,668b1. This platform provided a uniform lateral rotation path for the cutting head screens and geometrically compounded the circular movements of the cutting blades underneath the perforated screens. The combination of these circular movements produced a shaving performance that surpassed the performance of multiple circular and straight movements of the entire shaver body in all directions. They removed the escape paths for disoriented hairs, ended the need for repeated movements of the shaver body and ended the need to rotate or manipulate the shaver in order to reach irregular face areas. Furthermore, the time and effort required for a close shave with a rotary shaver was drastically reduced. Unlike the shaving action of other rotary shavers, the shaving action of the rotating platform described herein is demonstrable. Upon contact with the skin, the area under the platform's cutting heads is instantly shaved clean, without any movement of the shaver body. With all other rotary shavers, the hair ends will remain uncut if the shaver is placed upon the skin surface without movement of the entire shaver body.